Effective interaction between molecules in the BEC regime of a superfluid Fermi gas

We investigate the effective interaction between Cooper-pair molecules in the st rong-coupling BEC regime of a superfluid Fermi gas with a Feshbach resonance. Our work uses a path integral formulation and a renormalization group (RG) analy sis of fluctuations in a single-channel model. We show that a physical cutoff en ergy $\omega_c$ originating from the finite molecular binding energy is the key to understanding the interaction between molecules in the BEC regime. Our work t hus clarifies recent results by showing that $a_{\rm M}=2a_{\rm F}$ is a {\it ba re} molecular scattering length while $a_{\rm M}=(0.6\sim0.75) a_{\rm F}$ is the low energy molecular scattering length renormalized to include high-energy scat tering up to $\omega_c$ (here $a_{\rm F}$ is the scattering length between Fermi atoms). We also include many-body effects at finite temperatures. We find that $a_{\rm M}$ is strongly dependent on temperature, vanishing at $T_{\rm c}$, consistent with the earlier Bose gas results of Bijlsma and Stoof.